QSSOR and cubic non-polynomial spline method for the solution of two- point boundary value problems
Two-point boundary value problems are commonly used as a numerical test in developing an efficient numerical method. Several researchers studied the application of a cubic non-polynomial spline method to solve the two-point boundary value problems. A preliminary study found that a cubic non-polynomi...
| Main Authors: | , , , , |
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| Format: | Proceedings |
| Language: | English English |
| Published: |
IOP Publishing Ltd.
2021
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| Subjects: | |
| Online Access: | https://eprints.ums.edu.my/id/eprint/34631/1/ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/34631/2/FULLTEXT.pdf |
| Summary: | Two-point boundary value problems are commonly used as a numerical test in developing an efficient numerical method. Several researchers studied the application of a cubic non-polynomial spline method to solve the two-point boundary value problems. A preliminary study found that a cubic non-polynomial spline method is better than a standard finite difference method in terms of the accuracy of the solution. Therefore, this paper aims to examine the performance of a cubic non-polynomial spline method through the combination with the full-, half-, and quarter-sweep iterations. The performance was evaluated in terms of the number of iterations, the execution time and the maximum absolute error by varying the iterations from full-, half-to quarter-sweep. A successive over-relaxation iterative method was implemented to solve the large and sparse linear system. The numerical result showed that the newly derived QSSOR method, based on a cubic non-polynomial spline, performed better than the tested FSSOR and HSSOR methods. |
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